List of Publications

  [1] On the existence and regularity of fundamental domains with least boundary area,
         J. Differential Geom. 29 (1989), 623-663. PDF
  [2] The isoperimetric inequality for a minimal surface with radially connected boundary,
         Ann. Scuola Norm. Sup. Pisa (4), 17 (1990), 583-593. PDF
  [3] Index, vision number, and stability of complete minimal surfaces,
         Arch. Rat. Mech. Anal. 109 (1990), 195-212. PDF
  [4] On the analytic reflection of a minimal surface,
         Pacific J. Math. 157 (1993), 29-35. PDF
  [5] Isoperimetric inequalities on minimal submanifolds of space forms (with R. Gulliver),
         Manuscripta Math. 77 (1992), 169-189. PDF
  [6] The sharp isoperimetric inequality for minimal surfaces with radially connected boundary in hyperbolic
         space (with R. Gulliver), Inventiones Math. 109 (1992), 495-503. PDF
  [7] Sharp isoperimetric inequalities for stationary varifolds and area minimizing flat chains mod k,
         Kodai Math. J. 19 (1996), 177-190. PDF
  [8] Every stationary polyhedral set in R^n is area minimizing under diffeomorphisms,
         Pacific J. Math. 175 (1996), 439-446. PDF
  [9] On the existence of higher dimensional Enneper's surface,
         Comment. Math. Helvetici 71 (1996), 556-569. PDF
[10] The isoenergy inequality for a harmonic map,
        Houston J. Math. 24 (1998), 649-654. PDF
[11] Nonexistence of certain complete minimal surfaces with planar ends (with M. Soret),
        Comment. Math. Helvetici 75 (2000), 189-199. PDF
[12] The isoperimetric inequality for minimal surfaces in a Riemannian manifold,
        J. reine angewandte Math. 506 (1999), 205-214. PDF
[13] Sufficient conditions for constant mean curvature surfaces to be round,
        Math. Ann. 323 (2002), 143-156. PDF
[14] Embedded minimal surfaces and total curvature of curves in a manifold (with R. Gulliver),
        Math. Res. Letters 10 (2003), 343-362. PDF
[15] Relative isoperimetric inequality for domains outside a convex set,
        Archives Inequalities Appl. 1 (2003), 241-250. PDF
[16] Isoperimetric Inequalities of Minimal Submanifolds, Global Theory of Minimal Surfaces,
        Clay Math. Proceedings 2 (2005), 325-369. PDF  Streaming Video of my MSRI Lecture
[17] The relative isoperimetric inequality in Cartan-Hadamard 3-manifolds (with M. Ritore),
        J. reine angewandte Math. 605 (2007), 179-191. PDF
[18] The double cover relative to a convex set and the relative isoperimetric inequality,
        J. Aust. Math. Soc. 80 (2006), 375-382. PDF
[19] Total Positive curvature of hypersurfaces with convex boundary (with M. Ghomi and M. Ritore),
        J. Differential Geom. 72 (2006), 129-147. PDF
[20] The relative isoperimetric inequality outside a convex domain in R^n (with M. Ghomi and M. Ritore),
        Calc. Var. PDE. 29 (2007), 421-429. PDF
[21] First eigenvalue of symmetric minimal surfaces in S^3 (with M. Soret),
        Indiana Univ. Math. J. 58 (2009), 269-282. PDF
[22] Capillary surfaces in a convex cone (with S.-H. Park), Math. Zeitschrift 267 (2011), 875-886. PDF
[23] Higher dimensional minimal submanifolds generalizing the catenoid and helicoid (with J. Hoppe),
        Tohoku Math. J. 65 (2013), 43-55. PDF
[24] Noncommutative minimal surfaces (with J. Arnlind and J. Hoppe), Lett. Math. Phys. 106 (2016), 1109-1129.
        PDF  LMP
[25] New minimal surfaces in S^3 desingularizing the Clifford tori (with M. Soret), Math. Ann. 364 (2016),
        763-776. PDF
[26] Stable capillary hypersurfaces in a wedge (with M. Koiso), Pacific J. Math. 280 (2016), 1-15. PDF
[27] On the area of minimal surfaces in a slab (with B. Daniel), Int. Math. Res. Notices 2016 (2016), 7201-7211.
[28] Density of a minimal submanifold and total curvature of its boundary (with R. Gulliver), Comm. Anal. Geom.
        25 (2017), 545-556. PDF
[29] Mean curvature in manifolds with Ricci curvature bounded from below (with A. Fraser), Comment. Math.
        Helv. 93 (2018), 55-69. PDF
[30] Higher dimensional Schwarz's surfaces and Scherk's surfaces (with J. Hoppe), Calc. Var. (2018) 57:107. PDF
[31] Characterizing the harmonic manifolds by the eigenfunctions of the Laplacian (with S. Kim and J. Park),
        J. Geom. Phys. 126 (2018), 22-26. PDF
[32] Some minimal submanifolds generalizing the Clifford torus (with J. Hoppe), Math. Nach. 291 (2018), 2536-2542. PDF
[33] The minimality of determinantal varieties (with M. Bordemann and J. Hoppe), J. reine angew. Math. 773 (2021), 153-164. PDF
[34] The periodic Plateau problem and its application. PDF, arXiv:2104.09087
[35] Generating Axially Symmetric Minimal Hyper-surfaces in R^{1,3} (with J. Hoppe and O.T. Turgut). PDF, arXiv:2211.03887
[36] Complete minimal surfaces of finite topology in the doubled Schwarzschild 3-manifold
       (with Jaehoon Lee and Eungbeom Yeon). PDF, arXiv:2307.04625v1

Survey Papers

[S1] The History of the Plateau Problem,
         Proceedings of Workshop in Pure Mathematics, 12 (1992), 69-90. PDF
[S2] Characterizing the sphere in terms of volume, area, eigenvalues, and energy,
         Proceedings of Workshop in Pure Mathematics, 17 (1997), 5-17. PDF
[S3] The isoperimetric inequality of a minimal surface,
         Proceedings of the Second International Workshop on Differential Geometry, 2 (1998), 55-66. PDF
[S4] In search of nonexistent minimal surfaces,
         Trends in Mathematics, 1 (1998), 183-187. PDF
[S5] Ray preserving metrics and applications,
         Proceedings of the Sixth International Workshop on Differential Geometry, 6 (2002), 61-72. PDF
[S6] Minimal surfaces in S^3 and Yau's conjecture,
         Proceedings of the 10th International Workshop on Differential Geometry, 10(2005), 183-188. PDF
[S7] Radial viewpoint on minimal surfaces,     Surveys in Geometric Analysis and Relativity, 59-72,
         Advanced Lectures in Mathematics, International Press. PDF